國立高雄大學圖資館 |

Language: English

Back

Calculus of variations

Rindler, Filip.

Calculus of variations

Record Type:	Electronic resources : Monograph/item
Title/Author:	Calculus of variationsby Filip Rindler.
Author:	Rindler, Filip.
Published:	Cham :Springer International Publishing :2018.
Description:	xii, 444 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Calculus of variations.
Online resource:	http://dx.doi.org/10.1007/978-3-319-77637-8
ISBN:	9783319776378$q(electronic bk.)

Calculus of variations
Rindler, Filip.

Calculus of variations[electronic resource] /by Filip Rindler. - Cham :Springer International Publishing :2018. - xii, 444 p. :ill. (some col.), digital ;24 cm. - Universitext,0172-5939. - Universitext..

Part I Basic Course -- 1 Introduction -- 2 Convexity -- 3 Variations -- 4 Young Measures -- 5 Quasiconvexity -- 6 Polyconvexity -- 7 Relaxation -- Part II Advanced Topics -- 8 Rigidity -- 9 Microstructure -- 10 Singularities -- 11 Linear-Growth Functionals -- 12 Generalized Young Measures -- 13 G-Convergence -- A Prerequisites -- References -- Index.

This textbook provides a comprehensive introduction to the classical and modern calculus of variations, serving as a useful reference to advanced undergraduate and graduate students as well as researchers in the field. Starting from ten motivational examples, the book begins with the most important aspects of the classical theory, including the Direct Method, the Euler-Lagrange equation, Lagrange multipliers, Noether's Theorem and some regularity theory. Based on the efficient Young measure approach, the author then discusses the vectorial theory of integral functionals, including quasiconvexity, polyconvexity, and relaxation. In the second part, more recent material such as rigidity in differential inclusions, microstructure, convex integration, singularities in measures, functionals defined on functions of bounded variation (BV), and Γ-convergence for phase transitions and homogenization are explored. While predominantly designed as a textbook for lecture courses on the calculus of variations, this book can also serve as the basis for a reading seminar or as a companion for self-study. The reader is assumed to be familiar with basic vector analysis, functional analysis, Sobolev spaces, and measure theory, though most of the preliminaries are also recalled in the appendix.

ISBN: 9783319776378$q(electronic bk.)

Standard No.: 10.1007/978-3-319-77637-8doiSubjects--Topical Terms:

191127
Calculus of variations.

LC Class. No.: QA315 / .R563 2018

Dewey Class. No.: 515.64

Calculus of variations
LDR:02674nmm a2200349 a 4500 001 540767
003 DE-He213
005 20190110141938.0
006 m d
007 cr nn 008maaau
008 190308s2018 gw s 0 eng d
020 $a 9783319776378$q(electronic bk.)
020 $a 9783319776361$q(paper)
024 7 $a 10.1007/978-3-319-77637-8 $2 doi
035 $a 978-3-319-77637-8
040 $a GP $c GP
041 0 $a eng
050 4 $a QA315 $b .R563 2018
072 7 $a PBKQ $2 bicssc
072 7 $a PBU $2 bicssc
072 7 $a MAT005000 $2 bisacsh
072 7 $a MAT029020 $2 bisacsh
082 0 4 $a 515.64 $2 23
090 $a QA315 $b .R579 2018
100 1 $a Rindler, Filip. $3 819215
245 1 0 $a Calculus of variations $h [electronic resource] / $c by Filip Rindler.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2018.
300 $a xii, 444 p. : $b ill. (some col.), digital ; $c 24 cm.
490 1 $a Universitext, $x 0172-5939
505 0 $a Part I Basic Course -- 1 Introduction -- 2 Convexity -- 3 Variations -- 4 Young Measures -- 5 Quasiconvexity -- 6 Polyconvexity -- 7 Relaxation -- Part II Advanced Topics -- 8 Rigidity -- 9 Microstructure -- 10 Singularities -- 11 Linear-Growth Functionals -- 12 Generalized Young Measures -- 13 G-Convergence -- A Prerequisites -- References -- Index.
520 $a This textbook provides a comprehensive introduction to the classical and modern calculus of variations, serving as a useful reference to advanced undergraduate and graduate students as well as researchers in the field. Starting from ten motivational examples, the book begins with the most important aspects of the classical theory, including the Direct Method, the Euler-Lagrange equation, Lagrange multipliers, Noether's Theorem and some regularity theory. Based on the efficient Young measure approach, the author then discusses the vectorial theory of integral functionals, including quasiconvexity, polyconvexity, and relaxation. In the second part, more recent material such as rigidity in differential inclusions, microstructure, convex integration, singularities in measures, functionals defined on functions of bounded variation (BV), and Γ-convergence for phase transitions and homogenization are explored. While predominantly designed as a textbook for lecture courses on the calculus of variations, this book can also serve as the basis for a reading seminar or as a companion for self-study. The reader is assumed to be familiar with basic vector analysis, functional analysis, Sobolev spaces, and measure theory, though most of the preliminaries are also recalled in the appendix.
650 0 $a Calculus of variations. $3 191127
650 1 4 $a Mathematics. $3 184409
650 2 4 $a Calculus of Variations and Optimal Control; Optimization. $3 274198
650 2 4 $a Partial Differential Equations. $3 274075
650 2 4 $a Functional Analysis. $3 274845
650 2 4 $a Mathematical Applications in the Physical Sciences. $3 522718
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
830 0 $a Universitext. $3 558272
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-77637-8
950 $a Mathematics and Statistics (Springer-11649)